Combinatorics of non-ambiguous trees

4Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

Abstract

This article investigates combinatorial properties of non-ambiguous trees. These objects we define may be seen either as binary trees drawn on a grid with some constraints, or as a subset of the tree-like tableaux previously defined by Aval, Boussicault and Nadeau. The enumeration of non-ambiguous trees satisfying some additional constraints allows us to give elegant combinatorial proofs of identities due to Carlitz, and to Ehrenborg and Steingrímsson. We also provide a hook formula to count the number of non-ambiguous trees with a given underlying tree. Finally, we use non-ambiguous trees to describe a very natural bijection between parallelogram polyominoes and binary trees. © 2014 Elsevier Inc.

Cite

CITATION STYLE

APA

Aval, J. C., Boussicault, A., Bouvel, M., & Silimbani, M. (2014). Combinatorics of non-ambiguous trees. Advances in Applied Mathematics, 56(1), 78–108. https://doi.org/10.1016/j.aam.2013.11.004

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free